Stochastic processes and temporal rules

This article tries to give an answer to a fundamental question in temporal data mining: "Under what conditions a temporal rule extracted from an up-to-date temporal data keeps its cofidence/support on future data". A possible solution is given by using, on the one hand, a temporal logic formalism which allows the definition of the main notions (event, temporal rule, confidence) in a formal way and, on the other hand, the stochastic limit theory. Under this probabilistic temporal framework, the equivalence between the existence of the support of a temporal rule and the law of large numbers is systematically analyzed.